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Multi-class classification with a very large number of classes, or extreme classification, is a challenging problem from both statistical and computational perspectives. Most of the classical approaches to multi-class classification,…
We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this…
We study the design of efficient approximation algorithms for the $\ell$-center clustering and minimum-diameter $\ell$-clustering problems in high dimensional Euclidean and Hamming spaces. Our main tool is randomized dimension reduction.…
Approximate nearest neighbor search (ANNS) is a fundamental problem in databases and data mining. A scalable ANNS algorithm should be both memory-efficient and fast. Some early graph-based approaches have shown attractive theoretical…
Nearest-neighbour retrieval is central to classification and explainable-AI pipelines, but current practice relies on hand-tuning feature layers and distance metrics. We propose Targeted Manifold Manipulation-Nearest Neighbour (TMM-NN),…
In scenarios involving text classification where the number of classes is large (in multiples of 10000s) and training samples for each class are few and often verbose, nearest neighbor methods are effective but very slow in computing a…
Low-dimensional embeddings are essential for machine learning tasks involving graphs, such as node classification, link prediction, community detection, network visualization, and network compression. Although recent studies have identified…
Clustering-based Approximate Nearest Neighbor Search (ANNS) organizes a set of points into partitions, and searches only a few of them to find the nearest neighbors of a query. Despite its popularity, there are virtually no analytical tools…
Approximate $k$-nearest neighbor (AKNN) search is a fundamental problem with wide applications. To reduce memory and accelerate search, vector quantization is widely adopted. However, existing quantization methods either rely on codebooks…
With the growing integration of structured and unstructured data, new methods have emerged for performing similarity searches on vectors while honoring structured attribute constraints, i.e., a process known as Filtering Approximate Nearest…
Nearest neighbor (NN) problem is an important scientific problem. The NN query, to find the closest one to a given query point among a set of points, is widely used in applications such as density estimation, pattern classification,…
We give new data-dependent locality sensitive hashing schemes (LSH) for the Earth Mover's Distance ($\mathsf{EMD}$), and as a result, improve the best approximation for nearest neighbor search under $\mathsf{EMD}$ by a quadratic factor.…
In this paper we develop a new machinery to study the capacity of artificial neural networks (ANNs) to approximate high-dimensional functions without suffering from the curse of dimensionality. Specifically, we introduce a concept which we…
The network embedding task is to represent the node in the network as a low-dimensional vector while incorporating the topological and structural information. Most existing approaches solve this problem by factorizing a proximity matrix,…
We consider the problem of finding high dimensional approximate nearest neighbors. Suppose there are d independent rare features, each having its own independent statistics. A point x will have x_{i}=0 denote the absence of feature i, and…
Video anomaly detection (VAD) mainly refers to identifying anomalous events that have not occurred in the training set where only normal samples are available. Existing works usually formulate VAD as a reconstruction or prediction problem.…
Approximate Nearest Neighbor Search (ANNS) is a fundamental operation in vector databases, enabling efficient similarity search in high-dimensional spaces. While dense ANNS has been optimized using specialized hardware accelerators, sparse…
Dimensionality reduction is a fundamental task in modern data science. Several projection methods specifically tailored to take into account the non-linearity of the data via local embeddings have been proposed. Such methods are often based…
Exact nearest neighbor search is a computationally intensive process, and even its simpler sibling -- vector retrieval -- can be computationally complex. This is exacerbated when retrieving vectors which have high-dimension $d$ relative to…
We focus on the problem of identifying samples in a set that do not conform to structured patterns represented by low-dimensional manifolds. An effective way to solve this problem is to embed data in a high dimensional space, called…